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641.
We obtain a global estimate for the weak solution to an elliptic partial differential equation of -Laplacian type with BMO coefficients in a Lipschitz domain with small Lipschitz constant.
642.
Yoshiharu Kohayakawa Vojtěch Rödl Mathias Schacht Papa Sissokho 《Journal of Combinatorial Theory, Series A》2007,114(4):631-657
The generalized Turán number ex(G,H) of two graphs G and H is the maximum number of edges in a subgraph of G not containing H. When G is the complete graph Km on m vertices, the value of ex(Km,H) is , where o(1)→0 as m→∞, by the Erd?s-Stone-Simonovits theorem.In this paper we give an analogous result for triangle-free graphs H and pseudo-random graphs G. Our concept of pseudo-randomness is inspired by the jumbled graphs introduced by Thomason [A. Thomason, Pseudorandom graphs, in: Random Graphs '85, Poznań, 1985, North-Holland, Amsterdam, 1987, pp. 307-331. MR 89d:05158]. A graph G is (q,β)-bi-jumbled if
643.
In this paper, we study the existence of periodic solutions of the second order differential equations x″+f(x)x′+g(x)=e(t). Using continuation lemma, we obtain the existence of periodic solutions provided that F(x) () is sublinear when x tends to positive infinity and g(x) satisfies a new condition where M, d are two positive constants. 相似文献
644.
Yoshiharu Kohayakawa Vojtěch Rödl Mathias Schacht Endre Szemerédi 《Advances in Mathematics》2011,(6):5041
In 1983, Chvátal, Trotter and the two senior authors proved that for any Δ there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph KN with N?Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Δ. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and edges, with N=⌈B′n⌉ for some constant B′ that depends only on Δ. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Δ is . Our approach is based on random graphs; in fact, we show that the classical Erd?s–Rényi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Δ.The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. 相似文献
645.
Daniela Kühn Richard Mycroft Deryk Osthus 《Journal of Combinatorial Theory, Series B》2011,101(6):415-447
Sumner?s universal tournament conjecture states that any tournament on 2n−2 vertices contains a copy of any directed tree on n vertices. We prove an asymptotic version of this conjecture, namely that any tournament on (2+o(1))n vertices contains a copy of any directed tree on n vertices. In addition, we prove an asymptotically best possible result for trees of bounded degree, namely that for any fixed Δ, any tournament on (1+o(1))n vertices contains a copy of any directed tree on n vertices with maximum degree at most Δ. 相似文献
646.
J. Djoko Kamdem 《Mathematical Methods in the Applied Sciences》2011,34(12):1487-1498
In this work, we study the structural stability of the fully implicit Euler scheme for the Brinkman‐Forchheimer equations. More precisely, we consider the time discretization scheme of the unsteady Brinkman–Forchheimer equations, and we prove the existence of solutions. Moreover, we derive somebia priori estimates of the discrete in time solutions. Next, with the aid of the discrete Gronwall lemma, we show that the numerical solutions depend continuously on the Brinkman and the Forchheimer coefficient. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
647.
Ibrahima N’Doye Michel Zasadzinski Mohamed Darouach Nour-Eddine Radhy Abdelhaq Bouaziz 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7333-7341
In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall–Bellman lemma approach. The nonlinear systems under consideration can be non Lipschitz. Two cases are treated for the exponential stabilization: the static state feedback and the static output feedback. The robustness of the proposed control laws with regards to parameter uncertainties is also studied. A numerical example is given to show the effectiveness of the proposed method. 相似文献
648.
Douglas R. Woodall 《Journal of Graph Theory》2011,66(2):98-103
A graph G with maximum degree Δ and edge chromatic number χ′(G)>Δ is edge‐Δ‐critical if χ′(G?e)=Δ for every edge e of G. It is proved here that the vertex independence number of an edge‐Δ‐critical graph of order n is less than . For large Δ, this improves on the best bound previously known, which was roughly ; the bound conjectured by Vizing, which would be best possible, is . © 2010 Wiley Periodicals, Inc. J Graph Theory 66:98‐103, 2011 相似文献
649.
吕登峰 《数学的实践与认识》2011,41(2)
研究了一类带Sobolev-Hardy临界指数的奇异椭圆方程,应用变分方法,通过能量估计和证明对应的能量泛函满足(PS)_c条件,运用山路引理得到了这类方程非平凡解的存在性. 相似文献
650.
对单复变中的Schwarz引理与Schwarz-Pick引理在C~n中的超球上进行了推广.考虑C~n中单位球B_n上模小于1的全纯函数f(z),并在f(0)=0的条件下给出函数在原点的任意阶导数的估计.更进一步地,得到了B_n上模小于1的任意全纯函数在任意点的高阶导数的估计. 相似文献